Mathematics
The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method.
Take the assumed mean as 45. Give your answer correct to 2 decimal places.
| Number of patients | Number of days |
|---|---|
| 10 – 20 | 5 |
| 20 – 30 | 2 |
| 30 – 40 | 7 |
| 40 – 50 | 9 |
| 50 – 60 | 2 |
| 60 – 70 | 5 |
Measures of Central Tendency
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Answer
We construct the following table, taking assumed mean a = 45.
| Number of patients | Number of days (fi) | Class mark (xi) | di = xi - A | fidi |
|---|---|---|---|---|
| 10 – 20 | 5 | 15 | -30 | -150 |
| 20 – 30 | 2 | 25 | -20 | -40 |
| 30 – 40 | 7 | 35 | -10 | -70 |
| 40 – 50 | 9 | a=45 | 0 | 0 |
| 50 – 60 | 2 | 55 | 10 | 20 |
| 60 – 70 | 5 | 65 | 20 | 100 |
| Total | ∑ fi = 30 | ∑fi di = -140 |
By formula,
Hence, average number of patients attending the hospital per month is 40.33.
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